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• W2012156956 abstract "Using power series methods, Harris and Sibuya (3, 4) recently showed that if A: is an ordinary differential field of characteristic zero and y 5? 0 is an element of a differential extension of fc such that y and l/y satisfy linear differential equations with coefficients in fc, then y'iy is algebraic over fc. Using differential galois theory, we generalize this and characterize those polynomial relations among solutions of linear differential equations that force these solutions to have algebraic logarithmic derivatives. We also show that if / is an algebraic function of genus > 1 and if y and f(y) or y and ei v satisfy linear differential equations, then y is an algebraic function. Proposition 1(a) is obtained by letting n = 3, m2 = m^ = 1 and yi = 1. Proposition 1(b) is obtained by letting n = 2 and m2 = m. Sperber's techniques also allow him to handle solutions of certain nonlinear diferential equations. In this paper we prove results that imply" @default.
• W2012156956 created "2016-06-24" @default.
• W2012156956 creator A5071271321 @default.
• W2012156956 date "1986-02-01" @default.
• W2012156956 modified "2023-09-28" @default.
• W2012156956 title "Algebraic relations among solutions of linear differential equations" @default.
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• W2012156956 doi "https://doi.org/10.1090/s0002-9947-1986-0833707-x" @default.
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